A global assessment of the mixed layer in coastal sediments and implications for carbon storage

The sediment-water interface in the coastal ocean is a highly dynamic zone controlling biogeochemical fluxes of greenhouse gases, nutrients, and metals. Processes in the sediment mixed layer (SML) control the transfer and reactivity of both particulate and dissolved matter in coastal interfaces. Here we map the global distribution of the coastal SML based on excess 210Pb (210Pbex) profiles and then use a neural network model to upscale these observations. We show that highly dynamic regions such as large estuaries have thicker SMLs than most oceanic sediments. Organic carbon preservation and SMLs are inversely related as mixing stimulates oxidation in sediments which enhances organic matter decomposition. Sites with SML thickness >60 cm usually have lower organic carbon accumulation rates (<50 g C m−2 yr−1) and total organic carbon/specific surface area ratios (<0.4 mg m−2). Our global scale observations reveal that reworking can accelerate organic matter degradation and reduce carbon storage in coastal sediments.


Supplementary Methods 1: Data collection
We collected a total of 12 factors that may influence the formation of SML: water depth, mean annual precipitation, relative sea level rise rate, tropical cyclone frequency, mean tidal range, sediment accumulation rate, total suspended matter, chlorophyll-a concentration, primary productivity, bottom stress, river sediment load and river discharge. The individual Pearson correlation coefficients between these factors and SML are shown in the Supplementary Fig. 2 below. The raw data of all input parameters are shown in Supplementary Data 1.
Here we present a detailed data development for bottom stress and river discharge. Tidal currents and wind waves are the dominant driving forces for sediment re-suspension and transport in the bottom boundary layer of shallow seas. In general, the shear stress is calculated using the approximate formula τ=ρC-d U 2 , C-d≈3×10 -3 is seabed friction coefficient 1 . The tidal current speed is from TPXOv9 calculated from satellite altimeters 2 . The bottom orbital velocity beneath waves is calculated using the ECMWF Reanalysis v5 (ERA5) dataset 3 . We obtained multi-year mean observed river discharge data of global major rivers from the dataset by Milliman 4 . Then the global annual mean ocean circulation is calculated using the HYCOM high-resolution reanalysis ocean current dataset GOFS 3.1 [5][6][7] . The convection diffusion equation is used to calculated the river diluted water spread using the discharge data and circulation data.
Supplementary Fig. 2. The relationship between 12 influencing factors and thickness of sediment mixed layer (SML). The proposed five variables that best controlled SMLs thickness, marked in purple, were used to train the neural network model.

Supplementary Discussion 2: Influencing factors of sediment mixed layer
Plots of simulated SML thicknesses vs. bottom stress and primary production ( Supplementary  Fig. 3 below), illustrate the relative importance of physical and biological driving forces in different regions. The highest SMLs were linked with the highest bottom stress in large river estuaries, such as the Amazon estuary, which is about 120,000 Pa with SMLs thicknesses of almost 2 m. Thickness of SMLs also increased in regions with high primary productivity (3000 -5000 mg/m 2 /day) and weak physical forces (e.g., bottom stress of 0-1000Pa), such as the coast of north Colombia and Venezuela, which SML thickness is usually around 30 cm. Plot of measured SMLs and predicted SMLs ( Supplementary Fig. 4), showing a significant linear correlation relationship (0.73), which further corroborates our model evaluation metrics.

Supplementary Methods 2: Average sediment mixed layer
We conducted 100 global simulations and obtained a global average SML thickness each time. From these simulations, a probability distribution diagram was made ( Supplementary Fig. 5), with an associated mean value and standard error.
Supplementary Fig. 5. Probability distribution of the modeled average thickness of sediment mixed layer (SML) which ranged from 7~10 cm; this result is derived from 100 simulations in our model.

Supplementary Discussion 3: Sediments in global ocean
An additional 7800 data points were added in regions with poor data coverage, such as the English Channel, Hudson Bay and the China coastal seas. This was used to develop a new digital map of sediments-type distribution in the global ocean, based on the method of Dutkiewicz et al. 8 (Supplementary Fig. 6). Supplementary Methods 3: The Neural Network model MAE (equation [1]) and R 2 score (equation [2]) were used to evaluate the neural network model. The smaller the MAE and the larger the R 2 , the better the model.

Supplementary
Where n stands for the number of data points, is the target value, and is the predicted value.
Where n stands for the number of data points, is the target value, is the predicted value, and is average of target values. Five algorithms were chosen to simulate the global SML, including K-nearest neighbor (KNN), support vector machine (SVM), random forest (RF), gradient boosting regression (GBR) and multilayer perceptron (MLP); this was used to train and test our data respectively. These algorithms have very different principles and applicable fields. Through the comparison of these results (